Comparison between variational Monte Carlo and shell model calculations of neutrinoless double beta decay matrix elements in light nuclei
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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
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Squeezed States, Uncertainty Relations and the Pauli Principle in Composite and Cosmological Models
The importance of not only uncertainty relations but also the Pauli exclusion principle is emphasized in discussing various 'squeezed states' existing in the universe. The contents of this paper include: (1) Introduction; (2) Nuclear Physics in the Quark-Shell Model; (3) Hadron Physics in the Standard Quark-Gluon Model; (4) Quark-Lepton-Gauge-Boson Physics in Composite Models; (5) Astrophysics and Space-Time Physics in Cosmological Models; and (6) Conclusion. Also, not only the possible breakdown of (or deviation from) uncertainty relations but also the superficial violation of the Pauli principle at short distances (or high energies) in composite (and string) models is discussed in some detail.
Terazawa, Hidezumi↗
Lifetimes of two- and four-neutron-hole states in 204 Pb and 206 Pb
The centroid-shift method was used to determine half-lives of excited levels in 204 Pb and 206 Pb. For the states with 𝐼 𝜋 = 12 + , 17 − , and 19 − in 204 Pb, values of 𝑇 1/2 = 4.9(3), 3.9(3), and 0.9(3) ns, respectively, were determined. The half-life of the 𝐼 𝜋 = 9 − level in 206 Pb was measured to be 1.1(3) ns. In 204 Pb, the 12 + state arises from two neutron holes in the 𝑖 13/2 subshell, while the 17 − and 19 − levels are built on 𝜈(𝑖$^{−3}_{13/2}$, 𝑝$^{−1}_{1/2}$) and 𝜈(𝑖$^{−3}_{13/2}$, 𝑓$^{−1}_{5/2}$) four-neutron-hole configurations, respectively. The 9 − state in 206 Pb results from a 𝜈(𝑖$^{−1}_{13/2}$, 𝑓${−1}_{5/2}$) excitation. As a result, the transition probabilities for the decay of these isomeric levels are reasonably consistent with the expected single-particle values, and these states are described well by shell-model calculations using the kshell code with the KHHE interaction.
190 ≤ A ≤ 219↗
Accessing the Single-Particle Structure of the Pygmy Dipole Resonance in 208 Pb
New experimental data on the neutron single-particle character of the Pygmy Dipole Resonance (PDR) in Pb 208 are presented. They were obtained from ( d , p ) and resonant proton scattering experiments performed at the Q3D spectrograph of the Maier-Leibnitz Laboratory in Garching, Germany. The new data are compared to the large suite of complementary, experimental data available for Pb 208 and establish ( d , p ) as an additional, valuable, experimental probe to study the PDR and its collectivity. Furthermore, besides the single-particle character of the states, different features of the strength distributions are discussed and compared to large-scale shell model (LSSM) and energy-density functional plus quasiparticle-phonon model theoretical approaches to elucidate the microscopic structure of the PDR in Pb 208 .
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Probing the limits of statistical neutron capture for the r process: Experimental constraints on 141 Cs nuclear level densities
The r-process abundance peaks, particularly near mass number A ∼ 130, reflect underlying nuclear structure effects such as closed neutron shells, yet modeling the nucleosynthesis in this region remains hindered by uncertain neutron-capture rates. These rates are especially sensitive to nuclear level densities (NLDs) and γ-ray strength functions of neutron-rich nuclei, where experimental data are scarce. We present the first experimental constraint on the NLD of 141 Cs using the β-Oslo method, extending sensitivity to the neutron-rich regime near the N = 82 closed shell. Our data allow for critical calibration of microscopic NLD models and reveal that 141 Cs lies near the limit of statistical model applicability. Using this experimental input, we evaluate radiative neutron-capture rates across neighboring isotones using both Hauser–Feshbach (HF) and High Fidelity Resonance (HFR) models. Our results show order-of-magnitude rate increases for nuclei along the N = 86 line, signaling a transition to resonance-dominated capture in this region. These findings underscore the importance of constraining NLDs to improve r-process reaction network predictions, particularly in environments where the validity of statistical models breaks down.
Nuclear level density↗
Mapping of fragmented νf 5/2 →πf 7/2 transitions in the 73 Co→ 73 Ni decay
Excited states in 73 , 75 Ni were investigated through the β decay of 73 , 75 Co in an experiment performed at the National Superconducting Cyclotron Laboratory (NSCL) at Michigan State University (MSU). The experimental results extended the level scheme of Ni 73 to 3.2-MeV excitation energy and provided the experimental information on excited states in Ni 75 . The β -delayed neutron branching ratio for Co 73 was obtained. Furthermore, the experimental results are discussed in comparison with shell-model calculations.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
In-beam γ-ray spectroscopy of 68 Fe from charge exchange on 68 Co projectiles
Excited states in the neutron-rich nucleus 68 Fe were populated using a 9 Be( 68 Co, 68 Fe + γ)X charge-exchange reaction at 95 MeV/u. The new γ-ray transitions reported here for the first time complement data from β-decay studies and nucleon knockout reactions. In comparison to shell-model calculations with the LNPS effective interaction, two candidate states for the $6$$^{+}_{1}$ level emerge. Here, the distinct population pattern of excited states and the magnitude of the cross section, σ inc = 0.51(6) mb, make this reaction a promising one for future in-beam γ -ray spectroscopy. Reaction calculations with nuclear structure input from a new, locally optimized Hamiltonian, f7j4a, together with general considerations for heavy-ion-induced charge-exchange reactions appear consistent with most of the observations, although challenges remain.
59 ≤ A ≤ 89↗
Triaxiality and the nature of low-energy excitations in Ge 76
The deformation properties of the low-lying states in 76 Ge have been investigated following a safe energy Coulomb excitation measurement with the GRETINA tracking array and CHICO2 heavy-ion counter at the ATLAS accelerator facility at Argonne National Laboratory. A comprehensive set of transition and static E2 matrix elements were extracted from the measured differential Coulomb cross-sections, and compared with results of configuration interaction shell-model calculations and computations carried out within the framework of the generalized triaxial rotor model. The remarkable agreement between the calculated and experimental data supports a near-maximum triaxial deformation for the ground state of 76 Ge. Additionally, the degree of softness of the asymmetry in 76 Ge and 76 Se was investigated using rotational invariants generated from configuration interaction shell-model wave functions computed with the jj44b and JUN45 effective interactions. The resulting invariants are shown to be consistent with a stiff triaxial deformation in 76 Ge and a predominantly soft triaxial potential for 76 Se, in agreement with the conclusions of recent works by this collaboration.
59 ≤ A ≤ 89↗
Single-particle and dipole excitations in Co 62
An extensive study of the level structure of 62 Co has been performed following a complex multinucleon transfer reaction, 26 Mg( 48 Ca, 2α3npγ) 62 Co, at beam energies of 275, 290, and 320 MeV. The combination of the Gammasphere array, the fragment mass analyzer, and a focal-plane ionization chamber was used to identify and delineate excited levels in 62 Co. A considerable extension to the 62 Co level scheme is proposed with firm spin-parity values assigned on the basis of angular distribution and correlation analyses. Here, various level sequences built upon states of single-particle character have been observed, and an interpretation of these structures in the framework of the spherical shell model is presented. At moderate spins, two dipole bands have been observed and, based on their phenomenological study, a possible magnetic rotation character is suggested. However, theoretical calculations performed using the particle rotor model support magnetic rotation for only one of these dipole bands.
59 ≤ A ≤ 89↗
Nucleonic shells and nuclear masses
The binding energy of an isotope is a sensitive indicator of the underlying shell structure as it reflects the net energy content of a nucleus. Since magic nuclei are significantly lighter, or more bound, compared to their neighbors, the presence of nucleonic shell structure makes an imprint on nuclear masses. In this study, using a carefully designed binding-energy indicator, we catalog the appearance of spherical and deformed shell and subshell closures throughout the nuclear landscape. After presenting experimental evidence for shell and subshell closures as seen through the lens of nuclear masses, we study the ability of global nuclear mass models to predict local binding-energy variations related to shell effects.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Limits on assigning a shape to a nucleus
The interpretation of nuclear observables in the laboratory frame in terms of the intrinsic deformation parameters β and γ is a classical theme in nuclear structure. Here we use the quadrupole invariants, calculated within the framework of the configuration-interaction shell model, to clarify the meaning and limitations of nuclear shapes. In this work we introduce a novel method that enables us to calculate accurately higher-order invariants and, therefore, the fluctuations in both β and γ. We find that the shape parameter β often has a non-negligible degree of softness and that the angle γ is usually characterized by large fluctuations, rendering its effective value not meaningful. Contrary to common belief, we conclude that doubly magic nuclei are not spherical, because the notion of a well-defined shape does not apply to them.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
An algebraic cluster model based on the harmonic oscillator basis
We discuss the semimicroscopic algebraic cluster model introduced recently, in which the internal structure of the nuclear clusters is described by the harmonic oscillator shell model, while their relative motion is accounted for by the Vibron model. The algebraic formulation of the model makes extensive use of techniques associated with harmonic oscillators and their symmetry group, SU(3). The model is applied to some cluster systems and is found to reproduce important characteristics of nuclei in the sd-shell region. An approximate SU(3) dynamical symmetry is also found to hold for the C-12 + C-12 system.
Levai, Geza↗
Tunable-fidelity wave functions for the ab initio description of scattering and reactions
Here, the no-core shell model (NCSM) is an ab initio method that solves the nuclear many-body problem by expanding the many-particle wave function into a (typically) harmonic oscillator basis and minimizing the energy to obtain the expansion coefficients. Extensions of the NCSM, such as its coupling with microscopic-cluster basis states, further allow for an ab initio treatment of light-ion nuclear reactions of interest for both astrophysics and nuclear technology applications. A downside of the method is the exponential scaling of the basis size with increasing number of nucleons and excitation quanta, which limits its applicability to mass A ≲ 16 nuclei, except for variants where the basis is further down-selected via some truncation scheme. We consider a basis selection method for the NCSM that was first introduced in the context of the large-scale shell model and captures the essential degrees of freedom of the nuclear wave function leading to a favorable complexity scaling for calculations and enabling ab initio reaction calculations in sd-shell nuclei. The particle configurations within the NCSM basis are ordered based on their contribution to the first moment of the Hamiltonian matrix that results from the projection onto the many-body basis. The truncation scheme then consists in retaining only the lowest-first-moment configurations, which typically contain only few many-body basis states (Slater determinants). As the energy threshold above which configurations are disregarded is increased, the size of the basis becomes an almost-continuous variable, allowing for tunable fidelity in the obtained wave functions. The resulting wave functions can then be used directly in ab initio reaction calculations. We present calculations for 7 Li and n + 12 C scattering using nucleon-nucleon interactions derived from chiral effective field theory and softened using the similarity renormalization group method. The obtained energy levels invariably demonstrate exponential convergence with the size of the basis, and we find improved convergence in scattering calculations. To demonstrate the possibilities enabled by the approach, we also present a first calculation for the scattering of neutrons from 24 Mg. The method presented in this work appears promising for future studies of nuclei with mass A > 16, opening multiple future research directions impacting both nuclear astrophysics and nuclear technology applications.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Cross-shell excited configurations in the structure of 34 Si
The cross-shell excited states of 34 Si have been investigated via β decays of the 4 − ground state and the 1 + isomeric state of 34 Al. Since the valence protons and valence neutrons occupy different major shells in the ground state as well as the intruder 1 + isomeric state of 34 Al, intruder levels of 34 Si are populated via allowed β decays. Spin assignments to such intruder levels of 34 Si were established through γ-γ angular correlation analysis for the negative-parity states. The configurations of such intruder states play crucial roles in our understanding of the N = 20 shell gap evolution. A configuration interaction model derived from the FSU Hamiltonian was utilized in order to interpret the intruder states in 34 Si. Furthermore, shell model interaction derived from a more fundamental theory with the valence space in medium similarity renormalization group method was also employed to interpret the structure of 34 Si.
20 ≤ A ≤ 38↗
Reinvestigation of the level structures of the even-even nuclei 90 Zr and 92 Zr
Excited states of 90 Zr and 92 Zr were investigated using the fusion reactions 6 Li + 89 Y and 14 N + 82 Se , respectively. Based on the experimental data, 5 and 18 new 𝛾 rays have been added to the level schemes of 90 Zr and 92 Zr , respectively. The level structures of 90 Zr and 92 Zr have been interpreted with shell-model calculations using the GWBXG and SNET effective interactions. The neutron core-breaking and the importance of the 1𝑔 7/2 and 1ℎ 11/2 orbits for high-spin states of 92 Zr were discussed. Finally, the excitation energy of the neutron core-breaking of nuclei in the 𝐴=90 region was compared.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Long-lived isomeric states and quasiparticle band structures in neutron-rich 162,164 Gd nuclei from β decay
Neutron-rich nuclei 162,164 Eu were produced by bombarding a proton beam on a 238 U target at the Holifield Radioactive Ion Beam Facility at Oak Ridge National Laboratory and mass separating the 162,164 Eu products. New level schemes and new γ-ray transitions of the daughters 162,164 Gd were identified from β-decay spectroscopy studies. Additionally, half-lives of the 162,164 Eu were remeasured to clarify the previous ambiguous results. Two quasiparticle band structures were built and compared with neighboring nuclei. The β and γ bands were extended in 162 Gd and a γ band was extended in 164 Gd. Half-lives of the isomeric states at (6 - ) 1449 keV in 162 Gd and (4 - ) 1096 keV in 164 Gd were measured to be 99(3) μs and 0.56(3) μs, respectively. Projected shell model calculations were performed and found to be in good agreement with all of the experimental data.
150 ≤ A ≤ 189↗
Measurements and computational analysis of the natural decay of 176 Lu
Background: Mainly because of its long half-life and despite its scientific relevance, spectroscopic measurements of 176 Lu forbidden β decays are very limited and lack formulation of shape factors. A direct precise measurement of its Q value is also presently unreported. In addition, the description of forbidden decays provides interesting challenges for nuclear theory. The comparison of precise experimental results with theoretical calculations for these decays can help to test underlying models and can aid the interpretation of data from other experiments. Purpose: Perform the first precision measurements of 176 Lu β-decay spectra and attempt the observation of its electron capture decays, as well as perform the first precision direct measurement of the 176 Lu β-decay Q value. Compare the shape of the precisely determined experimental β spectra to theoretical calculations, and compare the end point energy to that obtained from an independent Q value measurement. Method: Here, the 176 Lu β-decay spectra measurements and the search for electron capture decays were performed with an experimental setup that employed lutetium-containing scintillator crystals and a NaI(Tl) spectrometer for coincidence counting. The β decay Q value was determined via high-precision Penning trap mass spectrometry (PTMS) with the LEBIT facility at the National Superconducting Cyclotron Laboratory. The β-spectrum calculations were performed within the Fermi theory formalism with nuclear structure effects calculated using a shell model approach. Results: Both β transitions of 176 Lu were experimentally observed and corresponding shape factors formulated in their entire energy ranges. The search for electron capture decay branches led to an experimental upper limit of 6.3×10 –6 relative to its β decays. The 176 Lu β-decay and electron capture Q values were measured using PTMS to be 1193.0(6) and 108.9(8) keV, respectively. This enabled precise β end point energies of 596.2(6) and 195.3(6) keV to be determined for the primary and secondary β decays, respectively. The conserved vector current hypothesis was applied to calculate the relativistic vector matrix elements. The β-spectrum shape was shown to significantly depend on the Coulomb displacement energy and on the value of the axial vector coupling constant gA, which was extracted according to different assumptions. Conclusion: The implemented self-scintillation method has provided unmatched observations of 176 Lu, independently validated by the first direct measurements of its β-decay Q value by Penning trap mass spectrometry. Theoretical study of the main β transition led to the extraction of very different effective gA and log10f values, showing that a high-precision description of this transition would require a realistic nuclear structure with nucleus deformation.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Low-spin structure of the N = 82 nucleus Cs 137
Excited states in 137 Cs have been studied by using the near-barrier, single-proton transfer reaction 10 B( 136 Xe, 9 Beγ) 137 Cs in inverse kinematics and performing particle-γ and particle-γγ coincidence measurements. The low-spin level scheme of 137 Cs has been augmented: (i) The expected set of single-proton, seniority ν = 1 states has been delineated in its entirety; (ii) Another member of the v = 3 proton 0g 7/2 multiplet, a low-lying 9/2 + level, has been identified and this set of states now approaches completion; (iii) A second 9/2 + and a candidate 13/2 + level have been observed. Furthermore, the results are discussed in the framework of shell-model calculations in the proton 2s1 d 0 g 0 h shell.
74 ATOMIC AND MOLECULAR PHYSICS↗